2011/12/23 by Mathieu Sart, Sart, Mathieu
Mathematics · #62G05 #62M30 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62M30 #stat.TH
paper · pdf · doi:10.48550/arxiv.1112.5634
arxiv created 2013/06/13 · arxiv updated 2013/06/14
We observe n inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form s (⋅, x) where x is the covariate and where s is an unknown function. We propose a model selection approach where the models are used to approximate the multivariate function s. We show that our estimator satisfies an oracle-type inequality under very weak assumptions both on the intensities and the models. By using an Hellinger-type loss, we establish non-asymptotic risk bounds and specify them under several kind of assumptions on the target function s such as being smooth or a product function. Besides, we show that our estimation procedure is robust with respect to these assumptions.